Concept explainers
The flux of
Answer to Problem 33SEP
The flux of
Explanation of Solution
Write the formula for lattice constant
Here, the radius of the iron atom is
Write the formula for volume
Write the formula for Fick’s law of diffusion.
Here, flux or flow of atoms is
Conclusion:
Refer Table 3.2, “Selected metals that have the BCC crystal structure at room temperature (20°C) and their lattice constants and atomic radii”.
The atomic radius of iron is
Substitute
Substitute
The number of atoms per unit volume is expressed as follows.
The concentration of atoms at the surface
The concentration of atom at the distance of
Refer Table 5.2, “Diffusivities at 500°C and 1000°C for selected solute-solvent diffusion systems”.
The diffusivity of manganese in FCC iron at 500°C is
Here,
Substitute
Thus, the flux of
Want to see more full solutions like this?
Chapter 5 Solutions
Foundations of Materials Science and Engineering
- A 0.015M solution of hydrogen cyanate ,HOCN has a pH of 2.67arrow_forwardThe vacancy concentration for a metal A with an activation energy Q is 2x10-5. Calculate the vacancy concentration for a second metal B with activation energy 1.2Q. (This question has only one correct answer) а. 2.3 x 10-6 b. 4.3 x 10-5 O c. 1.3 x 10-6 d. 3.3 x 10-4arrow_forwardProblem 3 An FCC iron-carbon alloy initially containing 0.35 wt% C is exposed to an oxygen-rich and virtually carbon- free atmosphere at 1400 K (1127 °C). Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0 wt% C. (This process of carbon depletion is termed decarburization.) At what position will the carbon concentration be 0.15 wt% after a 10-h treatment? The value of D at 1400 K is 6.9 x 10¹¹ m²/s.arrow_forward
- In an electrochemical cell, a metal anode lost 0.227 g while a total volume of 0.08149 L of hydrogen gas was produced. The temperature was 298 K and the barometric pressure was 745.4 mm Hg. At 298 K, the vapor pressure of water is 23.8 mm Hg. How many moles of hydrogen gas were collected?arrow_forwardQUESTION 7 .An experiment is conducted to determine the variation of the diffusion coefficient as a function of temperature when carbon is diffused into BCC iron. The diffusion coefficient is measured at two different temperatures and is given by: Temp (°C) D (m2/s) 100 6.2 x 10-12 542 3.1 x 10-10 Calculate a value for the activation energy Qd (eV/atom) based on the experimental data?arrow_forwardCarbon idallowed to diffuse through a steel plate 23.1 mm thick. The concentrations of carbon at the two faces are0.71 gnand 01g whhare mataontant It the pre exponential and activation energy are 0.0000006 ms and 75453 Mmol respectively compute the temperature at which the diffution fa in 52 10 P Give your answer in degrees.Celsius to 1 decimal placearrow_forward
- .Nitrogen from a gaseous phase is to be diffused into pure iron at 669 °C. If the surface concentration is maintained at 1.0 wt% N, what will be the concentration (wt%) 0.9 mm from the surface after 6 hours? Given: Qd = 58 kJ/mol and Do = 6.2 x 10-7 m2/s. %3Darrow_forwardIn an Al casting ingot containing 2wt.% Cu, the content of Cu at grain boundaries has reached 12wt.%. How long this ingot should be held at 530 K to attain a difference of 10% in Cu concentration between center and boundary of the grains. The mean distance from the center of grains to the boundary is 100μm. Du= 3.9x10⁹ cm²/secarrow_forwardAn FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.0 wt%. If after 51 h the concentration of carbon is 0.35 wt% at a position 3.5 mm below the surface, determine the temperature at which the treatment was carried out. You will need to use data in the two tables below to solve this problem. Diffusing Species Fe Table 5.1 Tabulation of Error Function Values erf(z) 0 0.0282 0.0564 0.1125 Fe Z 0 0.025 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Table 5.2 A Tabulation of Diffusion Data Host Metal a-Fe (BCC) y-Fe (FCC) a-Fe 0.1680 0.2227 0.2763 0.3286 0.3794 y-Fe 0.4284 0.4755 0.5205 Z 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 Do(m²/s) 2.8 x 10-4 5.0 x 10-5 6.2 x 10-7 2.3 x 10-5 erf(z) 0.5633 0.6039 0.6420 0.6778 0.7112 0.7421 0.7707 0.7970 0.8209 0.8427 0.8802 0.9103 80 284 Z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Activation Energy Qa kJ/mol eVlatom 251…arrow_forward
- A mixture of species of A, B, and C is injected into a liquid chromatographic column with length of 20.0 cm. The obtained separation results are listed as follows: Please calculate the average number of theoretical plates from the data. Please round your result to whole number. The answer would be 2,153 (Need getting the answer)arrow_forwardDiffusion of carbon into BCC iron for 12 hours at a temperature of 500 °C results in a carbon concentration of 0.2 wt% at a depth 2 mm from the surface. How long would it take to get a concentration of 0.2 wt% at a depth 3 mm from the surface at 500 °C?arrow_forwardYou want to carburize a steel drill bit in the presence of methane. The drill bit initially has a uniform carbon concentration of 0.25 wt% and is to be treated at 950 oC (1750 oF). If the concentration of carbon at the surface is suddenly brought to and maintained at 1.20 wt%, how long will it take to achieve a carbon content of 0.80 wt% at a position 0.5mm below the surface? (The diffusion coefficient for carbon in iron at this temperature is 1.6 x 10-11 m2/s.)arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY